In digital communication system, signals are usually transmitted over channels having a limited bandwidth. For high-speed data transmission, such bandwidth limited channels result in inter-symbol interference (ISI). Wireline channels are also subject to frequency-selective fading, and wireless channels experience multipath propagation. Furthermore, in most digital communication systems, the frequency response of the channels is usually not known a priori. This makes it difficult to design optimum filters for modulators and demodulators. In addition, for most practical channels, the frequency-response characteristics are time-variant so it is not possible to design optimum fixed demodulation filters.
The solution to the ISI problem is to design a receiver that employs means for compensating or reducing the ISI in the received signal. The compensator for the ISI is called an equalizer. There are many types of equalizers known for practical digital communication systems, such as maximum-likelihood (ML) estimation based equalizers, linear filtering with adjustable coefficients, decision feedback equalizers (DFE), etc., see J. G. Proakis, Digital Communications, Fourth Edition, McGraw-Hill, New York, 2001.
In order to be used for unknown channels, the equalizers are usually adjustable to the channel response, and for time-variant channels, are adaptive to the time variations in the channel impulse response (CIR). This technique is called adaptive equalization of the signal received via the channel.
A least mean square (LMS) process is the most commonly used for adaptive equalizing because of its computational simplicity. The LMS process is based on minimizing the mean square error (MSE) between a transmitted signal and an estimate of that signal at an output of the equalizer.
The major disadvantage of the LMS process is that the convergence rate is dependent on the eigenvalue spread of the autocorrelation matrix of the received signal. In addition, the LMS process needs a relatively long sequence of symbols in a training signal during a training stage.
In order to obtain faster convergence, one can use a recursive least-square (RLS) process. Because this process needs to estimate the power of the transmitted signal, it is more complicated and involves additional parameters. This technique can also introduce an “overshot” or “out of convergence” problem when the received sequence of symbols in the training signal is not long enough to make a correct power estimation, see S. Chern, J. Horng, and K. M. Wong, “The Performance of the Hybrid LMS Adaptive Algorithm,” Signal Processing, Vol. 44, No. 1, pp. 67–88, June 1995. This problem usually occurs during the initial training stage, especially when the value of the step-size is large.
Therefore, there is a need for a reduced complexity system and method that improves equalization of a signal received via a channel of a communications system.